EV Integration

Scenario

An island power system with growing EV adoption over a 15-year planning horizon. Three vehicle categories — private sedans, commercial delivery vans, and public transit buses — each have distinct charging patterns and V2G participation rates. The optimizer schedules EV charging and determines whether V2G discharge can reduce peak generation needs.

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Prerequisites

• A working ESFEX installation with Julia backend configured
• A base system configuration YAML file (e.g., from the Getting Started tutorial)
• Demand and availability profile files for the system

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S-Curve Growth Model

ESFEX models EV fleet growth using a logistic (S-curve) function [53]: slow initial uptake, rapid mid-period growth, and eventual saturation.

The fleet size at year t is calculated as:

fleet(t) = initial_fleet * max_adoption / (1 + exp(-growth_rate * (t - mid_point_year)))

Where:

• initial_fleet: Number of vehicles at the base year (from ev_quantity)
• max_adoption: Maximum growth multiplier on the initial fleet (e.g., 30 means up to 30x)
• growth_rate: Controls how fast adoption accelerates (higher = steeper curve)
• mid_point_year: Year at which growth is fastest (inflection point)
• mid_point_fraction: Position of the inflection point within the planning horizon (0.5 = midpoint)

Growth Rate Examples

growth_rate	Adoption Speed	Typical Use Case
0.05	Very slow	Conservative policy, no subsidies
0.12	Moderate	Gradual transition with incentives
0.20	Fast	Aggressive policy, strong subsidies
0.30	Very fast	Mandated transition, ban on ICE sales

Max Adoption Examples

max_adoption	Meaning	Scenario
5	5x initial fleet	Low electrification
15	15x initial fleet	Moderate electrification
30	30x initial fleet	Near-full electrification
50	50x initial fleet	Growth beyond current vehicle stock

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Configuration

Complete YAML Example

systems:
  island:
    # ... (nodes, generators, batteries, etc.)

    # ── EV Categories ──────────────────────────────────────────────
    ev_categories:
      sedan:
        battery_capacity_kwh: 60.0
        max_charge_power_kw: 11.0         # Level 2 AC charging
        max_discharge_power_kw: 7.0       # V2G discharge limit
        charging_power: 11.0              # Used for profile generation (kW)
        v2g_power: 7.0                    # V2G power per vehicle (kW)
        v2g_participation: 0.30           # 30% of parked sedans participate in V2G
        charge_efficiency: 0.95
        discharge_efficiency: 0.92
        min_soc: 0.20                     # Never discharge below 20%
        max_soc: 0.90                     # Never charge above 90%
        v2g_compensation: 0.05            # $/kWh compensation to EV owners
        max_adoption: 30.0                # Up to 30x initial fleet
        growth_rate: 0.12                 # Moderate adoption speed
        mid_point_fraction: 0.5           # Inflection at year 7-8 of 15

      commercial_van:
        battery_capacity_kwh: 80.0
        max_charge_power_kw: 22.0         # Level 2 fast AC
        max_discharge_power_kw: 15.0
        charging_power: 22.0
        v2g_power: 15.0
        v2g_participation: 0.15           # Lower V2G -- commercial use priority
        charge_efficiency: 0.94
        discharge_efficiency: 0.91
        min_soc: 0.25                     # Higher minimum for delivery reliability
        max_soc: 0.90
        v2g_compensation: 0.06
        max_adoption: 20.0
        growth_rate: 0.10
        mid_point_fraction: 0.55          # Slightly later adoption than sedans

      electric_bus:
        battery_capacity_kwh: 300.0
        max_charge_power_kw: 50.0         # DC fast charging at depot
        max_discharge_power_kw: 30.0
        charging_power: 50.0
        v2g_power: 30.0
        v2g_participation: 0.50           # High V2G -- centrally managed fleets
        charge_efficiency: 0.93
        discharge_efficiency: 0.90
        min_soc: 0.30                     # Higher reserve for public service
        max_soc: 0.85
        v2g_compensation: 0.08
        max_adoption: 15.0                # Public transit grows more slowly
        growth_rate: 0.08
        mid_point_fraction: 0.45          # Earlier adoption (government-led)

    # ── Fleet Quantities (initial, per node) ───────────────────────
    ev_quantity:
      sedan: [500, 300, 200]              # Nodes 0, 1, 2
      commercial_van: [80, 50, 30]
      electric_bus: [20, 10, 5]

    # ── Initial State of Charge ────────────────────────────────────
    EV_initial_soc: [0.6, 0.6, 0.6]      # 60% SOC at start, per node

    # ── 24-Hour Base Charging Patterns ─────────────────────────────
    base_patterns:
      sedan:
        # Private vehicles: charge after work/overnight
        - [0.05, 0.05, 0.05, 0.05, 0.05, 0.10,   # 00-05: overnight trickle
           0.15, 0.10, 0.05, 0.05, 0.05, 0.05,    # 06-11: most at work
           0.05, 0.05, 0.10, 0.15, 0.20, 0.80,    # 12-17: return home
           0.90, 0.85, 0.70, 0.50, 0.30, 0.10]    # 18-23: evening charge peak

      commercial_van:
        # Commercial: charge overnight at depot, operate during day
        - [0.70, 0.70, 0.65, 0.60, 0.50, 0.20,   # 00-05: depot charging
           0.05, 0.0, 0.0, 0.0, 0.0, 0.0,         # 06-11: on delivery routes
           0.0, 0.0, 0.0, 0.0, 0.05, 0.10,         # 12-17: partial return
           0.20, 0.40, 0.60, 0.70, 0.70, 0.70]     # 18-23: return to depot

      electric_bus:
        # Public transit: charge at night depot, operate dawn-to-dusk
        - [0.80, 0.80, 0.80, 0.70, 0.50, 0.10,   # 00-05: depot charging
           0.0, 0.0, 0.0, 0.0, 0.0, 0.0,          # 06-11: morning routes
           0.0, 0.0, 0.0, 0.0, 0.0, 0.0,           # 12-17: afternoon routes
           0.05, 0.10, 0.30, 0.50, 0.70, 0.80]     # 18-23: return to depot

Pattern Design Guidelines

Base patterns represent the fraction of vehicles plugged in and charging at each hour (0.0 to 1.0):

Factor	Private Sedans	Commercial Vans	Public Buses
Peak charging hours	18:00-22:00	00:00-05:00	00:00-05:00
Operating hours	07:00-17:00	06:00-18:00	06:00-21:00
Charging location	Home/work	Depot	Depot
Pattern variability	High (diverse users)	Medium	Low (scheduled)

V2G Configuration Details

V2G [51] allows EVs to discharge back to the grid during peak demand or high-price periods [52]. Key parameters:

• v2g_participation: Fraction of parked vehicles willing to provide V2G (0.0 to 1.0). Centrally managed fleets (buses) have higher participation than private vehicles.
• v2g_power: Maximum discharge power per vehicle in kW. Typically lower than charge power to preserve battery health.
• v2g_compensation: Payment to vehicle owners per kWh discharged ($/kWh). Must be high enough to offset battery degradation costs.
• min_soc: Minimum state of charge — the optimizer cannot discharge below this level, ensuring vehicles retain enough range for their next trip.
• discharge_efficiency: Round-trip losses for V2G (typically 90-92%).

The effective V2G capacity at any hour is:

V2G_capacity = num_vehicles * v2g_participation * availability * v2g_power / 1000  [MW]

Where availability comes from the complement of the charging pattern (vehicles that are parked but not charging can provide V2G).

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Running the Simulation

# Run with verbose output
esfex run -c ev_system.yaml --years 15 -v

# Run with specific output directory
esfex run -c ev_system.yaml --years 15 -o results/ev_study/ -v

Expected console output during execution:

[INFO] Loading configuration: ev_system.yaml
[INFO] Generating EV profiles for 3 categories, 3 nodes, 15 years
[INFO]   sedan: 1000 initial vehicles, S-curve max_adoption=30.0, growth_rate=0.12
[INFO]   commercial_van: 160 initial vehicles, S-curve max_adoption=20.0, growth_rate=0.10
[INFO]   electric_bus: 35 initial vehicles, S-curve max_adoption=15.0, growth_rate=0.08
[INFO] EV demand added to total demand (optimizer handles V2G scheduling)
[INFO] Solving master problem (year 1/15)...
...

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Results Analysis

EV Charging Profiles Over Time

import h5py
import numpy as np

with h5py.File("results/ev_study/output.h5", "r") as f:
    print(f"{'Year':>6} {'Peak Charge (MW)':>18} {'Peak V2G (MW)':>16} "
          f"{'Total Charge (GWh)':>20} {'Total V2G (GWh)':>18}")
    print("-" * 82)

    for yr in [1, 3, 5, 8, 10, 12, 15]:
        grp = f"detailed_results/island/year_{yr:03d}"
        charging = f[f"{grp}/ev_charging"][:]
        v2g = f[f"{grp}/ev_v2g"][:]

        print(f"{yr:>6} {charging.max():>18.1f} {v2g.max():>16.1f} "
              f"{charging.sum() / 1000:>20.1f} {v2g.sum() / 1000:>18.1f}")

Expected output (approximate values for a 3-node island):

  Year  Peak Charge (MW)   Peak V2G (MW)  Total Charge (GWh)    Total V2G (GWh)
----------------------------------------------------------------------------------
     1               4.2             1.1                12.3               2.8
     3               6.8             1.9                20.1               4.6
     5              14.5             4.2                45.2              10.1
     8              38.2            11.0               118.5              27.3
    10              62.1            18.5               195.0              45.8
    12              78.4            23.1               248.2              58.0
    15              85.6            25.0               271.5              63.2

Note the S-curve shape: slow growth in years 1-3, rapid acceleration in years 5-10, and saturation by year 12-15.

Fleet Growth Impact on System Demand

with h5py.File("results/ev_study/output.h5", "r") as f:
    base = f["demand/island/base_demand"][:]
    ev = f["demand/island/ev_demand"][:]
    total = f["demand/island/total_demand"][:]

    print(f"Base peak demand:  {base.max():.1f} MW")
    print(f"EV peak demand:    {ev.max():.1f} MW")
    print(f"Total peak demand: {total.max():.1f} MW")
    print(f"EV share of peak:  {ev.max() / total.max():.1%}")
    print(f"EV share of energy: {ev.sum() / total.sum():.1%}")

V2G Revenue and Grid Contribution

with h5py.File("results/ev_study/output.h5", "r") as f:
    for yr in [5, 10, 15]:
        grp = f"detailed_results/island/year_{yr:03d}"
        v2g = f[f"{grp}/ev_v2g"][:]
        prices = f[f"{grp}/prices"][:]

        # V2G revenue (price * discharge volume)
        revenue = np.sum(v2g * prices)
        # V2G contribution to peak shaving
        peak_hour = np.argmax(prices)
        v2g_at_peak = v2g[peak_hour] if peak_hour < len(v2g) else 0

        print(f"Year {yr}:")
        print(f"  V2G revenue:           ${revenue:>12,.0f}")
        print(f"  V2G at system peak:    {v2g_at_peak:>8.1f} MW")
        print(f"  Total V2G energy:      {v2g.sum():>8.0f} MWh")

Hourly Charging Profile Visualization

import numpy as np

with h5py.File("results/ev_study/output.h5", "r") as f:
    # Extract a typical day (day 180, summer) for year 10
    grp = "detailed_results/island/year_010"
    charging = f[f"{grp}/ev_charging"][:]

    # Hours 4320 to 4344 = day 180
    day_start = 180 * 24
    day_end = day_start + 24
    day_profile = charging[day_start:day_end]

    print("Hour | Charging (MW) | Bar")
    print("-" * 50)
    for h in range(24):
        bar = "#" * int(day_profile[h] / 2)
        print(f"  {h:02d} | {day_profile[h]:>12.1f} | {bar}")

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Cost Implications of EV Integration

Cost Component	Effect of EVs	Direction
Generation capacity	More peak capacity needed for charging	Increases cost
RE investment	More solar/wind to serve EV load	Increases investment
Battery storage	V2G reduces need for grid batteries	Decreases investment
Fuel cost	Higher demand increases fossil fuel use	Increases cost
Curtailment	EVs can absorb excess RE (smart charging)	Decreases waste
Grid reinforcement	Higher peak loads stress transmission	Increases cost

To quantify cost impacts, compare runs with and without EV:

scenarios = {
    "No EV": "results/no_ev/output.h5",
    "With EV": "results/ev_study/output.h5",
}

for name, path in scenarios.items():
    with h5py.File(path, "r") as f:
        cost = f["summary_results/objectives"][:].sum()
        re_pen = f["summary_results/re_penetration"][-1]
        gen_inv = f["summary_results/gen_investment_power"][:].sum()
        bat_inv = f["summary_results/bat_investment_power"][:].sum()

        print(f"\n{name}:")
        print(f"  Total NPV:          ${cost:>14,.0f}")
        print(f"  Final RE penetration: {re_pen:>8.1%}")
        print(f"  Total gen investment: {gen_inv:>8.1f} MW")
        print(f"  Total bat investment: {bat_inv:>8.1f} MW")

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Practical Tips

1. Start small: Test with a single EV category (sedan) before adding commercial and bus categories. This simplifies debugging.

2. Avoid double-counting EV demand: When EV optimization is enabled, the optimizer schedules EV charging. Do not manually add ev_demand to total_demand — the runner handles this automatically.

3. Pattern sensitivity: Charging patterns strongly influence peak demand. Run sensitivity analysis on pattern shapes if uncertain about real-world behavior.

4. V2G economics: Set v2g_compensation above the estimated battery degradation cost (typically 0.03-0.08 $/kWh) to ensure realistic participation rates.

5. Node distribution: Distribute EV quantities across nodes proportionally to population or vehicle registration data. Uneven distribution reveals localized grid stress.

6. Growth rate calibration: Compare your S-curve parameters against historical EV adoption data from comparable regions. Norway (fast), EU average (moderate), and developing economies (slow) provide useful benchmarks.

7. Computational note: EV profiles are generated once at simulation startup and stored in memory. They do not add significant computation time beyond the additional demand they create.

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Key Takeaways

1. S-curve adoption [53]: Fleet growth starts slow, accelerates in mid-years, then saturates — matching real-world technology diffusion patterns.
2. Demand impact: EV charging becomes a significant fraction of total demand by year 10-15, potentially 15-30% of peak load.
3. V2G value: Bidirectional charging provides peak shaving and reserve services, partially offsetting the cost of serving EV demand.
4. Charging patterns: Off-peak charging (buses at night) is naturally aligned with low-cost hours and can absorb excess renewable generation.
5. Storage synergy: EV batteries complement stationary storage, potentially reducing grid-scale battery investment needs by 10-25%.
6. Category diversity: Different vehicle types (private, commercial, transit) have complementary charging patterns, smoothing aggregate demand.